Results Template

Clustering

Introduction

library(easystats)

summary(report::report(sessionInfo()))

The analysis was done using the R Statistical language (v4.0.2; R Core Team, 2020) on macOS Catalina 10.15.6, using the packages effectsize (v0.4.1), ggplot2 (v3.3.2), stringr (v1.4.0), forcats (v0.5.0), tidyr (v1.1.2), readr (v1.3.1), dplyr (v1.0.3), tibble (v3.0.6), purrr (v0.3.4), parameters (v0.10.1.1), insight (v0.11.1.1), see (v0.6.1.1), performance (v0.6.1.1), modelbased (v0.4.0), easystats (v0.2.0), correlation (v0.5.0), bayestestR (v0.8.0.1), report (v0.2.0) and tidyverse (v1.3.0).

Data

df <- read_csv("data/class_wide_1.csv")

> Parsed with column specification:
> cols(
>   .default = col_double(),
>   speaker = col_character(),
>   `54` = col_character()
> )

> See spec(...) for full column specifications.

Clustering

Introduction

In this task, individuals heard spoken speech tokens and freely classified them into groups. Using hierarchical clustering we aim to see what clusters or groups appear as a result of the free classification task.

library(here)

> here() starts at /Users/jgeller1/Desktop/clustering_project

library(tidyverse)  # data manipulation
library(cluster)    # clustering algorithms
library(factoextra) # clustering visualization

> Welcome! Want to learn more? See two factoextra-related books at https://goo.gl/ve3WBa

library(dendextend) # for comparing two dendrograms

> 
> ---------------------
> Welcome to dendextend version 1.14.0
> Type citation('dendextend') for how to cite the package.
> 
> Type browseVignettes(package = 'dendextend') for the package vignette.
> The github page is: https://github.com/talgalili/dendextend/
> 
> Suggestions and bug-reports can be submitted at: https://github.com/talgalili/dendextend/issues
> Or contact: <tal.galili@gmail.com>
> 
>   To suppress this message use:  suppressPackageStartupMessages(library(dendextend))
> ---------------------

> 
> Attaching package: 'dendextend'

> The following object is masked from 'package:stats':
> 
>     cutree

Data Preparation

1. Rows are observations (individuals) and columns are variables
2. Any missing value in the data must be removed or estimated.
3. The data must be standardized (i.e., scaled) to make variables comparable (I am not doing this here)

Read in the data

clust_data <- read_csv(here("data", "class_wide_1.csv")) # read in data

> Warning: Missing column names filled in: 'X1' [1]

> Parsed with column specification:
> cols(
>   .default = col_double(),
>   speaker = col_character(),
>   `54` = col_character()
> )

> See spec(...) for full column specifications.

clust_data <- select(clust_data, -X1, -`54`) # remove extra col sub 54 has weird formatting

clust_data <- as.data.frame(clust_data) # turn into df 

rownames(clust_data) <- clust_data$speaker # make row names speaker

clust_data <- select(clust_data,-speaker) # remove extra col sub 54 has weird formatting

head(clust_data)# show first couple rows

	8	7	1	10	11	12	14	15	16	17	18	19	2	20	23	25	26	27	28	29	3	30	31	32	33	34	35	36	38	4	40	41	42	43	44	45	46	47	48	49	5	50	51	52	53	55	56	58	59	6	78	87	90	91	96	105	110	111	115	121	123	125	132	133	135	148	151	152	153	155	156	157	158	159	160	161	162	163	164	165	166	167	168	169
bengali_9	1	5	5	1	11	2	1	8	4	2	2	1	9	7	4	5	1	1	1	11	5	1	7	7	9	8	10	8	1	3	1	10	1	1	12	1	5	1	5	8	1	3	7	1	8	9	1	1	5	9	1	11	1	11	1	6	11	1	2	1	9	1	3	1	1	1	5	1	8	4	8	6	5	1	5	1	7	4	1	5	1	7	1	2
bengali_13	6	5	5	7	14	4	2	7	4	2	6	3	9	1	4	5	4	2	3	11	12	1	8	11	9	8	10	11	1	4	12	1	1	8	11	1	5	4	1	8	5	4	7	3	8	9	1	8	11	7	1	11	1	11	1	6	11	7	8	6	9	1	6	2	3	6	9	1	8	4	10	6	5	2	1	14	7	6	4	5	1	4	2	4
bengali_16	1	5	5	7	7	4	3	6	2	8	3	3	3	1	3	4	6	1	3	10	2	1	7	8	9	8	10	11	6	3	8	8	1	8	11	1	1	2	5	7	5	4	7	3	8	9	8	1	6	7	5	11	2	6	1	6	10	6	8	6	10	10	4	2	3	1	7	4	8	11	8	6	3	2	3	14	7	7	1	5	1	7	4	4
gujarati_5	4	5	5	1	14	4	1	7	4	9	9	1	9	4	3	5	4	2	4	8	9	1	7	9	9	6	10	8	1	2	8	7	1	8	8	3	11	2	2	8	10	3	7	11	8	9	7	3	11	7	1	11	2	10	1	1	11	6	8	6	9	10	4	3	2	3	5	3	2	5	9	6	3	1	3	14	7	5	6	6	1	4	2	5
gujarati_13	1	5	5	1	15	4	2	8	4	2	6	1	9	4	5	5	6	2	4	8	5	1	7	9	9	8	10	2	1	2	12	1	1	8	11	1	11	6	5	8	2	4	7	1	8	9	7	10	5	7	1	11	2	11	1	6	11	2	8	6	9	10	4	2	1	1	5	1	2	5	9	6	3	1	4	14	7	5	6	5	1	7	3	6
gujarati_14	5	5	5	1	7	4	1	8	4	9	9	3	9	5	7	5	4	4	6	1	5	1	6	9	9	6	10	9	1	4	13	2	1	8	11	6	3	4	5	8	3	3	7	15	8	8	8	6	5	6	2	11	8	11	1	6	11	6	9	6	9	8	4	2	1	2	5	3	8	5	9	6	3	8	4	5	3	7	6	7	6	7	5	1

Agglomerative Hierarchical Clustering

I am going to cluster the data using average link clustering. Average link clustering computes all pairwise dissimilarities between the elements, and considers the average of these dissimilarities as the distance between clusters

# Dissimilarity matrix
d <- dist(clust_data, method = "euclidean")

# Hierarchical clustering using Average Linkage
hc1 <- hclust(d, method = "average" )

# Plot the obtained dendrogram
plot(hc1, cex = 0.6, hang = -1)

In the dendrogram displayed above, each leaf corresponds to one observation. As we move up the tree, observations that are similar to each other are combined into branches, which are themselves fused at a higher height.

The height of the fusion, provided on the vertical axis, indicates the (dis)similarity between two observations. The higher the height of the fusion, the less similar the observations are. Note that, conclusions about the proximity of two observations can be drawn only based on the height where branches containing those two observations first are fused. We cannot use the proximity of two observations along the horizontal axis as a criteria of their similarity.

The height of the cut to the dendrogram controls the number of clusters obtained. It plays the same role as the k in k-means clustering. In order to identify sub-groups (i.e. clusters), we can cut the dendrogram with cutree:

# Ward's method
hc5 <- hclust(d, method = "average" )

# Cut tree into 4 groups
sub_grp <- cutree(hc5, k = 3)

# Number of members in each cluster
table(sub_grp)

> sub_grp
>  1  2  3 
>  9 18 18

## sub_grp
##  1  2  3  4 
##  7 12 19 12

Visualize clusters on dendrogram

plot(hc5, cex = 0.6)
rect.hclust(hc5, k = 3, border = 2:5)

From this, we glean that 3 clusters seem to be adequate. Generally participants groups speakers into 3 clusters/groups:

• English/African into clust 1

• Indo/European into clust 2

• Asian into clust 3

clust_data <- clust_data %>%
  mutate(cluster = sub_grp)

fviz_cluster(list(data = clust_data, cluster = sub_grp))

Full Code

The full script of executive code contained in this document is reproduced here.

# Set up the environment (or use local alternative `source("utils/config.R")`)
source("https://raw.githubusercontent.com/RealityBending/TemplateResults/main/utils/config.R")  

fast <- FALSE  # Make this false to skip the chunks
library(easystats)

summary(report::report(sessionInfo()))
df <- read_csv("data/class_wide_1.csv")
report::cite_packages(sessionInfo())
library(here)
library(tidyverse)  # data manipulation
library(cluster)    # clustering algorithms
library(factoextra) # clustering visualization
library(dendextend) # for comparing two dendrograms


clust_data <- read_csv(here("data", "class_wide_1.csv")) # read in data

clust_data <- select(clust_data, -X1, -`54`) # remove extra col sub 54 has weird formatting

clust_data <- as.data.frame(clust_data) # turn into df 

rownames(clust_data) <- clust_data$speaker # make row names speaker

clust_data <- select(clust_data,-speaker) # remove extra col sub 54 has weird formatting

head(clust_data)# show first couple rows

# Dissimilarity matrix
d <- dist(clust_data, method = "euclidean")

# Hierarchical clustering using Average Linkage
hc1 <- hclust(d, method = "average" )

# Plot the obtained dendrogram
plot(hc1, cex = 0.6, hang = -1)


# Ward's method
hc5 <- hclust(d, method = "average" )

# Cut tree into 4 groups
sub_grp <- cutree(hc5, k = 3)

# Number of members in each cluster
table(sub_grp)
## sub_grp
##  1  2  3  4 
##  7 12 19 12

plot(hc5, cex = 0.6)
rect.hclust(hc5, k = 3, border = 2:5)


clust_data <- clust_data %>%
  mutate(cluster = sub_grp)

fviz_cluster(list(data = clust_data, cluster = sub_grp))

Package References

report::cite_packages(sessionInfo())

• Alboukadel Kassambara and Fabian Mundt (2020). factoextra: Extract and Visualize the Results of Multivariate Data Analyses. R package version 1.0.7. https://CRAN.R-project.org/package=factoextra
• Ben-Shachar, Makowski & Lüdecke (2020). Compute and interpret indices of effect size. CRAN. Available from https://github.com/easystats/effectsize.
• H. Wickham. ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York, 2016.
• Hadley Wickham (2019). stringr: Simple, Consistent Wrappers for Common String Operations. R package version 1.4.0. https://CRAN.R-project.org/package=stringr
• Hadley Wickham (2020). forcats: Tools for Working with Categorical Variables (Factors). R package version 0.5.0. https://CRAN.R-project.org/package=forcats
• Hadley Wickham (2020). tidyr: Tidy Messy Data. R package version 1.1.2. https://CRAN.R-project.org/package=tidyr
• Hadley Wickham, Jim Hester and Romain Francois (2018). readr: Read Rectangular Text Data. R package version 1.3.1. https://CRAN.R-project.org/package=readr
• Hadley Wickham, Romain François, Lionel Henry and Kirill Müller (2021). dplyr: A Grammar of Data Manipulation. R package version 1.0.3. https://CRAN.R-project.org/package=dplyr
• Kirill Müller (2017). here: A Simpler Way to Find Your Files. R package version 0.1. https://CRAN.R-project.org/package=here
• Kirill Müller and Hadley Wickham (2021). tibble: Simple Data Frames. R package version 3.0.6. https://CRAN.R-project.org/package=tibble
• Lionel Henry and Hadley Wickham (2020). purrr: Functional Programming Tools. R package version 0.3.4. https://CRAN.R-project.org/package=purrr
• Lüdecke D, Ben-Shachar M, Patil I, Makowski D (2020). “parameters:Extracting, Computing and Exploring the Parameters of StatisticalModels using R.” Journal of Open Source Software, 5(53), 2445. doi:10.21105/joss.02445 (URL: https://doi.org/10.21105/joss.02445).
• Lüdecke D, Waggoner P, Makowski D (2019). “insight: A Unified Interfaceto Access Information from Model Objects in R.” Journal of Open SourceSoftware, 4(38), 1412. doi: 10.21105/joss.01412 (URL:https://doi.org/10.21105/joss.01412).
• Lüdecke, Ben-Shachar, Waggoner & Makowski (2020). Visualisation Toolbox for ‘easystats’ and Extra Geoms, Themes and Color Palettes for ‘ggplot2.’ CRAN. Available from https://easystats.github.io/see/
• Lüdecke, Makowski, Waggoner & Patil (2020). Assessment of Regression Models Performance. CRAN. Available from https://easystats.github.io/performance/
• Maechler, M., Rousseeuw, P., Struyf, A., Hubert, M., Hornik, K.(2021). cluster: Cluster Analysis Basics and Extensions. R package version 2.1.1.
• Makowski, D., Ben-Shachar, M. S. & Lüdecke, D. (2020). Estimation of Model-Based Predictions, Contrasts and Means. CRAN.
• Makowski, D., Ben-Shachar, M. S. & Lüdecke, D. (2020). The {easystats} collection of R packages. GitHub.
• Makowski, D., Ben-Shachar, M. S., Patil, I., & Lüdecke, D. (2019). Methods and Algorithms for Correlation Analysis in R. Journal of Open Source Software, 5(51), 2306. 10.21105/joss.02306
• Makowski, D., Ben-Shachar, M., & Lüdecke, D. (2019). bayestestR: Describing Effects and their Uncertainty, Existence and Significance within the Bayesian Framework. Journal of Open Source Software, 4(40), 1541. doi:10.21105/joss.01541
• Makowski, D., Lüdecke, D., & Ben-Shachar, M.S. (2020). Automated reporting as a practical tool to improve reproducibility and methodological best practices adoption. CRAN. Available from https://github.com/easystats/report. doi: .
• R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
• Tal Galili (2015). dendextend: an R package for visualizing, adjusting, and comparing trees of hierarchical clustering. Bioinformatics. DOI: 10.1093/bioinformatics/btv428
• Wickham et al., (2019). Welcome to the tidyverse. Journal of Open Source Software, 4(43), 1686, https://doi.org/10.21105/joss.01686

References